Consider the TRS R consisting of the rewrite rule 1: app(app(app(compose,f),g),x) -> app(f,app(g,x)) There are 2 dependency pairs: 2: APP(app(app(compose,f),g),x) -> APP(f,app(g,x)) 3: APP(app(app(compose,f),g),x) -> APP(g,x) Consider the SCC {2,3}. By taking the polynomial interpretation [compose] = 1 and [app](x,y) = [APP](x,y) = x + y + 1, the rules in {1-3} are strictly decreasing. Hence the TRS is terminating.